Solve Radical Equations

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you isolate a variable in a radical equation?

Back

Square both sides of the equation to eliminate the radical, then solve for the variable.

Front

What is the first step in solving the equation √(x) = 10?

Back

Square both sides to get x = 100.

Front

What is the principle of squaring both sides of an equation?

Back

It allows you to eliminate the square root, but you must check for extraneous solutions.

Front

If √(x + 3) = 5, what is the value of x?

Back

x = 22.

Front

What should you do after solving a radical equation?

Back

Check your solutions by substituting them back into the original equation.

Front

What is an extraneous solution?

Back

A solution that does not satisfy the original equation after substitution.

Front

Solve the equation √(n) = 9. What is n?

Back

n = 81.

Front

How do you solve √(x - 1) = 3?

Back

Square both sides to get x - 1 = 9, then x = 10.

Front

What is the solution to the equation √(v + 4) = 7?

Back

v = 45.